[枚举]cf228b

B. Fox and Cross

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Fox Ciel has a board with n rows and n columns. So, the board consists of n × n cells. Each cell contains either a symbol '.', or a symbol '#'.

A cross on the board is a connected set of exactly five cells of the board that looks like a cross. The picture below shows how it looks.

Ciel wants to draw several (may be zero) crosses on the board. Each cross must cover exactly five cells with symbols '#', and any cell with symbol '#' must belong to some cross. No two crosses can share a cell.

Please, tell Ciel if she can draw the crosses in the described way.

Input

The first line contains an integer n (3 ≤ n ≤ 100) — the size of the board.

Each of the next n lines describes one row of the board. Thei-th line describes the i-th row of the board and consists of n characters. Each character is either a symbol '.', or a symbol '#'.

Output

Output a single line with "YES" if Ciel can draw the crosses in the described way. Otherwise output a single line with "NO".

Sample test(s)

Input

5.#...####..####...#......

Output

YES

Input

4################

Output

NO

Input

6.#....####...####..#.##.######.#..#.

Output

YES

Input

6.#..#.######.####..####.######.#..#.

Output

NO

Input

3.........

Output

YES

Note

In example 1, you can draw two crosses. The picture below shows what they look like.

In example 2, the board contains 16 cells with '#', but each cross contains 5. Since 16 is not a multiple of 5, so it's impossible to cover all.

从左往右从上往下扫描，容易证明，我们遇到的第一个点一定是一个十字的上顶点，把它涂掉，接下来遇到的第一个点一定也是一个十字的上顶点。

#include <cstdio>char map[110][110];int main(){int n;scanf("%d",&n);for (int i=1;i<=n;i++){for (int j=1;j<=n;j++){char tmp;do tmp = getchar();while (tmp!='.'&&tmp!='#');map[i][j] = tmp=='#';}}for (int i=1;i<=n;i++){for (int j=1;j<=n;j++){if (map[i][j]){if (map[i+1][j]&&map[i+2][j]&&map[i+1][j-1]&&map[i+1][j+1]){map[i][j]=map[i+1][j]=map[i+2][j]=map[i+1][j-1]=map[i+1][j+1] = false;}else{printf("NO");return 0;}}}}printf("YES");return 0;}